Chapter 13

Java Programming: From Problem Analysis to Program Design, 4e Chapter 13 Recursion

Chapter Objectives
Learn about recursive definitions
Explore the base case and the general case of a recursive definition
Learn about recursive algorithms
Java Programming: From Problem Analysis to Program Design, 4e

Chapter Objectives (continued)
Learn about recursive methods
Become aware of direct and indirect recursion
Explore how to use recursive methods to implement recursive algorithms

Recursive Definitions
Recursion
Process of solving a problem by reducing it to smaller versions of itself
Recursive definition
Definition in which a problem is expressed in terms of a smaller version of itself
Has one or more base cases

Recursive Definitions (continued) Java Programming: From Problem Analysis to Program Design, 4e

Recursive Definitions (continued)
Recursive algorithm
Algorithm that finds the solution to a given problem by reducing the problem to smaller versions of itself
Has one or more base cases
Implemented using recursive methods
Recursive method
Method that calls itself
Base case
Case in recursive definition in which the solution is obtained directly
Stops the recursion

Recursive Definitions (continued)
General solution
Breaks problem into smaller versions of itself
General case
Case in recursive definition in which a smaller version of itself is called
Must eventually be reduced to a base case

Tracing a Recursive Method
Recursive method
Logically, you can think of a recursive method having unlimited copies of itself
Every recursive call has its own:
Code
Set of parameters
Set of local variables

Tracing a Recursive Method (continued)
After completing a recursive call
Control goes back to the calling environment
Recursive call must execute completely before control goes back to previous call
Execution in previous call begins from point immediately following recursive call

Recursive Definitions
Directly recursive: a method that calls itself
Indirectly recursive: a method that calls another method and eventually results in the original method call
Tail recursive method: recursive method in which the last statement executed is the recursive call
Infinite recursion: the case where every recursive call results in another recursive call

Designing Recursive Methods
Understand problem requirements
Determine limiting conditions
Identify base cases

Designing Recursive Methods (continued)
Provide direct solution to each base case
Identify general case(s)
Provide solutions to general cases in terms of smaller versions of general cases

Recursive Factorial Method Java Programming: From Problem Analysis to Program Design, 4e public static int fact( int num) { if (num = = 0) return 1; else return num * fact(num – 1); }

Recursive Factorial Method (continued) Java Programming: From Problem Analysis to Program Design, 4e

Largest Value in Array Java Programming: From Problem Analysis to Program Design, 4e

Largest Value in Array (continued) Java Programming: From Problem Analysis to Program Design, 4e
if the size of the list is 1
the largest element in the list is the only element in the list
else
to find the largest element in list[a]...list[b]
a. find the largest element in list[a + 1]...list[b]
and call it max
b. compare list[a] and max
if ( list[a] >= max )
the largest element in list[a]...list[b] is
list[a]
else
the largest element in list[a]...list[b] is max

Largest Value in Array (continued) Java Programming: From Problem Analysis to Program Design, 4e public static int largest( int [] list, int lowerIndex, int upperIndex) { int max; if (lowerIndex == upperIndex) return list[lowerIndex]; else { max = largest(list, lowerIndex + 1, upperIndex); if (list[lowerIndex] >= max) return list[lowerIndex]; else return max; } }

Execution of largest (list, 0, 3) Java Programming: From Problem Analysis to Program Design, 4e

Recursive Fibonacci Java Programming: From Problem Analysis to Program Design, 4e

Recursive Fibonacci (continued) Java Programming: From Problem Analysis to Program Design, 4e public static int rFibNum( int a, int b, int n) { if (n == 1) return a; else if (n == 2) return b; else return rFibNum(a, b, n -1) + rFibNum(a, b, n - 2); }

Recursive Fibonacci (continued) Java Programming: From Problem Analysis to Program Design, 4e

Towers of Hanoi Problem with Three Disks Java Programming: From Problem Analysis to Program Design, 4e

Towers of Hanoi: Three Disk Solution Java Programming: From Problem Analysis to Program Design, 4e

Towers of Hanoi: Three Disk Solution (continued) Java Programming: From Problem Analysis to Program Design, 4e

Towers of Hanoi: Recursive Algorithm Java Programming: From Problem Analysis to Program Design, 4e public static void moveDisks( int count, int needle1, int needle3, int needle2) { if (count > 0) { moveDisks(count - 1, needle1, needle2, needle3); System.out.println( " Move disk " + count + " from needle " + needle1 + " to needle " + needle3 + " . " ); moveDisks(count - 1, needle2, needle3, needle1); } }

Recursion or Iteration?
Two ways to solve particular problem
Iteration
Recursion
Iterative control structures: use looping to repeat a set of statements
Tradeoffs between two options
Sometimes recursive solution is easier
Recursive solution is often slower

Programming Example: Decimal to Binary Java Programming: From Problem Analysis to Program Design, 4e

Sierpinski Gaskets of Various Orders Java Programming: From Problem Analysis to Program Design, 4e

Programming Example: Sierpinski Gasket
Input: nonnegative integer indicating level of Sierpinski gasket
Output: triangle shape displaying a Sierpinski gasket of the given order
Solution includes:
Recursive method drawSierpinski
Method to find midpoint of two points

Programming Example: Sierpinski Gasket (continued) Java Programming: From Problem Analysis to Program Design, 4e private void drawSierpinski(Graphics g, int lev, Point p1, Point p2, Point p3) { Point midP1P2; Point midP2P3; Point midP3P1; if (lev > 0) { g.drawLine(p1.x, p1.y, p2.x, p2.y); g.drawLine(p2.x, p2.y, p3.x, p3.y); g.drawLine(p3.x, p3.y, p1.x, p1.y); midP1P2 = midPoint(p1, p2); midP2P3 = midPoint(p2, p3); midP3P1 = midPoint(p3, p1); drawSierpinski(g, lev - 1, p1, midP1P2, midP3P1); drawSierpinski(g, lev - 1, p2, midP2P3, midP1P2); drawSierpinski(g, lev - 1, p3, midP3P1, midP2P3); } }

Programming Example: Sierpinski Gasket (continued) Java Programming: From Problem Analysis to Program Design, 4e

Chapter Summary
Recursive definitions
Recursive algorithms
Recursive methods
Base cases
General cases

Chapter Summary (continued)
Tracing recursive methods
Designing recursive methods
Varieties of recursive methods
Recursion vs. iteration
Various recursive functions explored

Chapter 13

by Terry Yoast on Aug 25, 2010

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